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The incipient infinite cluster in high-dimensional percolation
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Tarski's problem about the elementary theory of free
groups has a positive solution
Olga Kharlampovich, Alexei Myasnikov
Abstract.
We prove that the elementary theories of all nonabelian free groups
coincide and that the elementary theory of a free group is decidable.
These results answer two old questions that were raised by A. Tarski
around 1945.
Copyright 1998 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 04 (1998), pp. 101-108
- Publisher Identifier: S 1079-6762(98)00047-X
- 1991 Mathematics Subject Classification. Primary 20E05, 20F10
- Key words and phrases.Free group, elementary theory, Tarski
- Received by the editors May 25, 1998
- Posted on December 14, 1998
- Communicated by Efim Zelmanov
- Comments (When Available)
Olga Kharlampovich
Department of Mathematics and Statistics,
McGill University,
805 Sherbrooke St. West,
Montreal, QC, Canada H3A 2K6
E-mail address: olga@Math.McGill.CA
Alexei Myasnikov
Department of Mathematics,
City College,
Convent Ave. \& 138th St.,
New York, NY 10031
E-mail address: Alexei@rio.sci.ccny.cuny.edu
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